Steady state of a two-species annihilation process with separated reactants

Area of Science:

• Chemical Physics
• Statistical Mechanics
• Theoretical Chemistry

Background:

• Annihilation processes are fundamental in chemical reactions and physical phenomena.
• Understanding the interplay between diffusion, reaction rates, and deposition is crucial for predicting system behavior.

Purpose of the Study:

• To elucidate the steady-state behavior of a one-dimensional annihilation process involving two separated reactants.
• To identify key parameters governing the system's dynamics and regimes.
• To establish a unified method for describing the reaction kernel across different dynamical regimes.

Main Methods:

• Numerical and analytical investigations of a one-dimensional annihilation system.
• Analysis of particle density, gap length distribution, and marginal probabilities.
• Utilizing the probability of finding the rightmost A (RMA) and leftmost B (LMB) particles to describe the reaction kernel.

Main Results:

• A crossover between diffusion-limited (DL) and reaction-limited (RL) regimes was observed, dependent on parameter ratios.
• The probability p(x_A, x_B) of RMA and LMB positions serves as a key descriptor for the reaction process.
• The reaction kernel can be effectively approximated by p(x_A, x_B) in both DL and RL regimes, showing excellent agreement with numerical and analytical results.

Conclusions:

• The probability p(x_A, x_B) provides a robust framework for understanding annihilation dynamics across different regimes.
• In the DL regime, the reaction kernel relates to adjacent RMA and LMB particles.
• In the RL regime, the reaction kernel is influenced by the marginal probabilities of individual particle distributions.